A Cartesian ghost-cell multigrid Poisson solver for incompressible flows
A Cartesian ghost-cell multigrid Poisson solver for incompressible flows
复制标题
用于不可压缩流的笛卡尔鬼细胞多重网格泊松求解器
DOI：
10.1002/nme.2967
复制
发表时间：
2010
影响因子：
2.9
通讯作者：
Ma Z
中科院分区：
文献类型：
--
作者：
Ma Z
本文提出了一种用于模拟不可压缩流体流动的简单笛卡尔鬼细胞多网格泊松求解器。流场在浸入固体的矩形网格上进行了有效的离散。在实体边界附近分布着少量虚影网格单元及其对称图像单元。借助虚影和象元，可以有效地实现Dirichlet和Neumann边界条件。在求解Navier-Stokes方程时，采用了速度和压力耦合的Chorin分数阶投影法。采用逐点高斯-塞德尔迭代法求解压力泊松方程。为了加快求解到相应线性系统的收敛速度，还引入了嵌入鬼影和图像单元的亚级粗网格，并在顺序V循环中运行。为了证明该方法的准确性和有效性，本文给出了几个测试案例，包括经典的理想圆柱体不可压缩流动、盖子驱动的腔体流动和通过固定/旋转圆柱体的粘性流动。版权所有©2010 John Wiley & Sons， Ltd
In this paper, a simple Cartesian ghost‐cell multigrid Poisson solver is proposed for simulating incompressible fluid flows. The flow field is discretized efficiently on a rectangular mesh, in which solid bodies are immersed. A small number of ghost mesh cells and their symmetric image cells are distributed in the vicinity of the solid boundary. With the aid of the ghost and image cells, the Dirichlet and Neumann boundary conditions can be implemented effectively. Chorin's fractional‐step projection method is adopted for the coupling of velocity and pressure for the solution of the Navier–Stokes equations. Point‐wise Gauss–Seidel iteration is used to solve the pressure Poisson equation. To speed up the convergence of the solution to the corresponding linear system, sub‐level coarse meshes embedded with ghost and image cells are also introduced and operated in a sequential V‐cycle. Several test cases including the classical ideal incompressible flow around a cylinder, a lid‐driven cavity flow and viscous flow past a fixed/rotating cylinder are presented to demonstrate the accuracy and efficiency of the current approach. Copyright © 2010 John Wiley & Sons, Ltd.